The relative degree and large complete minors in infinite graphs

Maya Stein; José Zamora

doi:10.1016/j.endm.2011.05.023

The relative degree and large complete minors in infinite graphs

Maya Stein, José Zamora

Facultad Ciencias Exactas

Resultado de la investigación: Contribución a una revista › Artículo › revisión exhaustiva

Resumen

Finite graphs of large minimum degree have large complete (topological) minors. We propose a new and very natural notion, the relative degree of an end, which makes it possible to extend this fact to locally finite graphs and to graphs with countably many ends. We conjecture the extension to be true for all infinite graphs.

Idioma original	Inglés
Páginas (desde-hasta)	129-134
Número de páginas	6
Publicación	Electronic Notes in Discrete Mathematics
Volumen	37
N.º	C
DOI	https://doi.org/10.1016/j.endm.2011.05.023
Estado	Publicada - 1 ago 2011

Áreas temáticas de ASJC Scopus

Matemáticas discretas y combinatorias
Matemáticas aplicadas

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10.1016/j.endm.2011.05.023

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abstract = "Finite graphs of large minimum degree have large complete (topological) minors. We propose a new and very natural notion, the relative degree of an end, which makes it possible to extend this fact to locally finite graphs and to graphs with countably many ends. We conjecture the extension to be true for all infinite graphs.",

keywords = "Extremal graph theory, Infinite graph theory, Minimum degree, Minor, Relative degree, Topological minor",

author = "Maya Stein and Jos{\'e} Zamora",

note = "Funding Information: 1 Supported by Fondecyt project no. 2Email: mstein@dim.uchile.cl 3Email: josezamora@unab.cl",

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N2 - Finite graphs of large minimum degree have large complete (topological) minors. We propose a new and very natural notion, the relative degree of an end, which makes it possible to extend this fact to locally finite graphs and to graphs with countably many ends. We conjecture the extension to be true for all infinite graphs.

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KW - Extremal graph theory

KW - Infinite graph theory

KW - Minimum degree

KW - Minor

KW - Relative degree

KW - Topological minor

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